When the energy executive Dennis Bakke retired with a fortune from the AES Corporation, the company he co-founded, he and his wife, Eileen, decided to direct their attention and money to education.

Dennis and Eileen Bakke, the founders of Imagine Schools. Imagine is now the largest commercial manager of charter schools in the country.

Mrs. Bakke, a former teacher, said she had been interested in education since the summer she was a 12-year-old and, together with a friend, opened the Humpty Dumpty Day School, charging $2 a week in “tuition” to parents of the children attending. Mr. Bakke was eager to experiment with applying business strategies and discipline to public schools.

The Bakkes became part of the nation’s new crop of education entrepreneurs, founding a commercial charter school company called Imagine Schools. Beginning with one failed charter school company they acquired in 2004, they have built an organization that has contracts with 71 schools in 11 states and the District of Columbia. Imagine is now the largest commercial manager of charter schools in the country.

But as Imagine continues to expand, it is coming under growing scrutiny from school boards and state regulators questioning how public money is spent and whether the company exerts too much control over the schools.

The concerns are being raised as charters, designed by education reformers to create alternatives to hidebound and failing public schools, are becoming an indelible part of the nation’s education landscape. Such schools are among the biggest beneficiaries of the billions of dollars the Obama administration plans to spend to improve public education.

Because public money is used, most states grant charters to run such schools only to nonprofit groups with the expectation that they will exercise the same independent oversight that public school boards do. Some are run locally. Some bring in nonprofit management chains. And a number use commercial management companies like Imagine.

But regulators in some states have found that Imagine has elbowed the charter holders out of virtually all school decision making — hiring and firing principals and staff members, controlling and profiting from school real estate, and retaining fees under contracts that often guarantee Imagine’s management in perpetuity.

The arrangements, they say, allow Imagine to use public money with little oversight. “Under either charter law or traditional nonprofit law, there really is no way an entity should end up on both sides of business transactions,” said Marc Dean Millot, publisher of the report K-12 Leads and a former president of the National Charter Schools Alliance, a trade association, now defunct, for the charter school movement.

“Imagine works to dominate the board of the charter holder, and then it does a deal with the board it dominates — and that cannot be an arm’s length transaction,” he said.

Such concerns have thwarted efforts by Imagine to open a school in Florida, threaten to stall its push into Texas, and have ended its business with a school in Georgia and another in New York, as well as other states.

Imagine is not shy about the way it wields its power, which it calls essential to its governing philosophy. “Imagine Schools operates the entire school, and is not a consultant or management company,” its Web site says. “All principals, teachers, and staff are Imagine Schools people. The Imagine Schools culture is meant to permeate every aspect of the school’s life.”

Mrs. Bakke, who is paid $100,000 as vice president of education at Imagine, says it works in “close partnership” with the boards of the schools it manages. “The governing boards are definitely in charge, but they look to us, frankly, because as you know, nonprofit boards are well meaning but don’t always have the experience and expertise running the schools,” she said in an interview.

She said that she and her husband, who is paid $200,000 as the company’s chief executive, sank $155 million into Imagine and that they were able to run schools efficiently. “We offer a great deal for communities and for taxpayers,” Mrs. Bakke said, “because we’re providing education at less than what a traditional school is spending.”

She says the company should be judged by its educational results, not its business and financial arrangements.

As measured by testing mandated under the No Child Left Behind law, the academic achievements of schools managed by Imagine are mixed, like those of most charter schools. But Imagine says that many students in the schools it manages enter with academic abilities below their grade level and that a better measurement of its success is the rate at which they are catching up.

Its analysis of test data taken at the beginning and end of the 2008-9 school year shows that 89 percent of its schools had learning gains better than public schools serving similar populations of students.

Mrs. Bakke said her company “is operated as a not-for-profit.” But Imagine is not a nonprofit group, and it has so far failed to gain status as a charity from the I.R.S.

Imagine applied for federal tax exemption in 2005 and has repeatedly said approval is imminent. It typically takes four to six months for such approvals. “We’re not sure why it’s taking so long,” said Mrs. Bakke, who is 56. “We suspect it’s because we’re trailblazers in a sense, and they haven’t had an application quite like this.”

The I.R.S., as is its policy, declined to comment.

The lack of status as a federally approved nonprofit group is proving to be one of Imagine’s biggest challenges. So it often gets involved with schools at their inception, recruiting board members or hitching its wagon to nonprofit groups that can obtain a charter, as it did in Las Vegas, where it teamed with 100 Black Men of Las Vegas to open an elementary school, the 100 Academy of Excellence. The school opened in 2006, and the county school board soon began documenting problems. It found the school’s bookkeeping under Imagine to be lax, and it said that the school lacked enough licensed teachers.

The school has had three principals in four years, two of whom were pressured to resign after complaining that there was not enough money for essentials like textbooks and a school nurse. The state said that by paying Imagine for necessities like furniture and computers, the school had violated regulations requiring competitive bidding. It further violated state law by running a deficit, which left it in debt to Imagine.

Mrs. Bakke declined to comment on issues raised at specific schools. “In all cases we strive to operate with high ethical standards, set high standards for performance, hire the best possible people, and correct mistakes as quickly as possible,” she wrote in an e-mail message.

Some schools say they are happy with Imagine’s management. At Hope Community Charter School in the District of Columbia, which opened in 2005 and where Imagine helped identify board members, the board agreed to pay Imagine virtually all of the school’s revenue, to allow Imagine to set the school’s budget subject only to approval that “shall not be unreasonably withheld or delayed,” and to seek Imagine’s approval for how it spends charitable gifts.

James Kemp, the board chairman, said that District of Columbia charter school regulators had repeatedly expressed concerns about the arrangements. He also said that even the school’s own auditors chided the board for allowing Imagine to pay several large bills without its approval, as required under contract.

“The charter board has alerted us and me specifically that this is not the normal way charter schools run, having their management company as involved as Imagine is with our school,” Mr. Kemp said. “But that’s the way we’ve set this up, and we’re happy with it.”

Josephine Baker, executive director of the District of Columbia Public Charter School Board, which grants and oversees charters in Washington, said the board had concerns about who was running the show at Hope Community.

“It’s not just Imagine, though Imagine is the one that probably has given us the most concern,” she said. “We find it is very hard for schools that hire management companies to maintain their independence, and charter schools are supposed to be independent.”

Mrs. Baker said she did not think the contract between Imagine and Hope Community would be approved today, in part because the entire model of using management companies is flawed. “There are not a whole lot of charter schools that are just marvelous, and those that are do not have management companies,” she said.

In Texas, parents trying to open a charter school for elementary school students thought that Imagine was going too far.

“Imagine did a few things that indicated they thought the charter belonged to them, which was not our understanding at all,” said Karelei Munn, who is part of a group working to establish a charter school in Georgetown, Tex., near Austin. “We were looking to control our board, and they were looking to control our board.”

Ms. Munn and other members of the group holding the charter broke their ties with Imagine and are trying to form a school on their own.

Regulators in Texas have been slow to approve a second Imagine school, citing concerns that include an e-mail message from Mr. Bakke to the company’s senior staff members that was reported on by The St. Louis Post-Dispatch last fall. In the message, dated Sept. 4, 2008, Mr. Bakke cautioned his executives against giving boards of schools the “misconception” that they “are responsible for making big decisions about budget matters, school policies, hiring of the principal and dozens of other matters.”

Mr. Bakke, who is 64, suggested requiring board members to sign undated letters of resignation or limiting board terms to a single year.

In a statement after the e-mail message was disclosed, Mr. Bakke apologized to board members “who felt offended or maligned,” saying he had “overstated my personal frustration in ensuring that the dedicated, caring people who hold the seats of charter governing boards at Imagine Schools understand and support our mission and operating philosophy.”

As Texas continues its consideration, the e-mail message helped upend Imagine’s plans to open a school in the Hillsborough County School District in Florida, which encompasses Tampa.

“That e-mail was very, very bad for them,” said Jenna Hodgens, the local supervisor of charter schools. “All the things we had been questioning, things about control of the school, he answered in his own words.”

The Hillsborough school board rejected the application in December. “Charter schools are not private schools, they are public schools and are governed as such,” said Susan Valdes, who heads the board. “Some, though, are starting to forget that — and they’re getting away with it. But not here.”

Fees, Rent and Bank Accounts

Some schools that have contracted with Imagine have feuded with the company over fees. Imagine typically charges 12 percent of a school’s revenue for basic services. It then may tack on fees, for example, for guaranteeing a school access to credit if needed or to cover the costs of flying Imagine personnel in to address problems.

The Kennesaw Charter School in Kennesaw, Ga., ended its contract with Imagine in February over such issues.

Under its original contract with Imagine, the Kennesaw school board forwarded all revenue it received from the state and district to a bank account in Florida controlled by Imagine to pay salaries and other expenses. Kennesaw’s board had full discretion over just $20,000, said Lori Hardegree, a board member.

If the school had money left over at the end of the year, the surplus was paid as a fee to Imagine.

Minutes of board meetings and reporting by the local school district show that the board had trouble getting information from Imagine about how it was using the money. And the school owed Imagine $1.2 million, in part for what the company spent to cover damage from a hurricane but also partly for expenses the company described as “off the books” and never fully accounted for to the school board’s or the district’s satisfaction.

It took Kennesaw more than a year of negotiations to break up with Imagine, and it still owes the company roughly $480,000. But board members say they are finding that they are saving money by running the school themselves.

“For one thing, we’re saving $30,000 that went out each month to pay Imagine’s fees,” Ms. Hardegree said. “We’re finding we’re saving money on every contract that we’re negotiating on our own.”

In New York, the Bronx Academy of Promise Charter School agreed to pay Imagine 12 percent of its revenue as a fee, and an additional 2.5 percent was charged to ensure Imagine would extend a loan to the school should it need one. The doors had hardly opened when the school’s board and principal began having problems with Imagine.

“It was rather baffling, but as a management company, they weren’t providing any management services,” said one person who has worked with the school and spoke anonymously for fear of retaliation. “With the exception of payroll processing and some accounting support, it wasn’t really clear what they were doing for the school.”

At the end of its first school year last May, Bronx Academy broke its contract with Imagine. Mrs. Bakke said that Imagine provided a full battery of educational, financial and administrative services to the Kennesaw school and the Bronx Academy. “Both boards were fully aware of start-up and other costs incurred by Imagine, and the obligation to repay those costs in the event of a termination of contract,” she wrote in an e-mail message.

The Ties That Bind

One of the most difficult tasks for a charter school is getting a building. Only a few cities like New York or Washington help such schools with real estate. And charter schools cannot use tax-exempt bonds to raise money the way public school systems can.

Mrs. Bakke said that Imagine’s real estate activities ease that burden for charter schools and are one of the biggest assets it brings to the table. “Our organization brings new investment into public education and avoids the need for the local community to float school bonds,” she wrote in an e-mail message.

But some regulators and school officials say that Imagine uses debt and real estate to bind schools to it.

Imagine typically buys or leases buildings through a real estate arm, SchoolhouseFinance, and uses those properties to attract groups wanting to open charter schools that then pay to rent them.

Last year, Imagine sold 27 of its school buildings to Entertainment Properties Trust, a real estate investment trust that is the country’s largest owner of movie theaters, as part of a deal that won the company $206 million. The buildings that were sold were leased back by Imagine, which then subleased them to the schools that occupy them.

Mrs. Bakke said a portion of the proceeds from the sale of those buildings was used to pay off bank debt and construction costs, with the remainder going to buy or construct new buildings and into the operations of existing schools. But board members of eight schools said they were never consulted about the sales or the decision by Imagine to commit them to leases. In at least some cases, Imagine makes money on the subleases. Bronx Academy, for example, paid Imagine $10,000 a month more in rent than the company paid the owner of its building.

The rents the company charges schools it manages now are one of the things threatening to scuttle its agreements with the two schools it manages in Nevada, the 100 Academy of Excellence and Imagine School in the Valle.

Last year, almost 40 percent of the $3.6 million that Nevada paid 100 Academy was spent on rent. Less than half of its total revenue, about 41 percent, was used to cover salaries and benefits for teachers and administrators, who are employees of Imagine.